A stochastic model for the development of Bateson-Dobzhansky-Muller incompatibilities that incorporates protein interaction networks.

Speciation is characterized by the development of reproductive isolating barriers between diverging groups. Intrinsic post-zygotic barriers of the type envisioned by Bateson, Dobzhansky, and Muller are deleterious epistatic interactions among loci that reduce hybrid fitness, leading to reproductive isolation. The first formal population genetic model of the development of these barriers was published by Orr in 1995, and here we develop a more general model of this process by incorporating finite protein-protein interaction networks, which reduce the probability of deleterious interactions in vivo. Our model shows that the development of deleterious interactions is limited by the density of the protein-protein interaction network. We have confirmed our analytical predictions of the number of possible interactions given the number of allele substitutions by using simulations on the Saccharomyces cerevisiae protein-protein interaction network. These results allow us to define the rate at which deleterious interactions are expected to form, and hence the speciation rate, for any protein-protein interaction network.